PUB - Publikationen an der Universität Bielefeld

Real fluids contain small thermodynamic fluctuations on small scales. These fluctuations, governed by fluctuation-dissipation relations, introduce what is known as fluctuating hydrodynamics. This thesis is dedicated to investigating large deviations and higher order fluctuation expansions for conservative stochastic partial differential equations arising from fluctuating hydrodynamics. In particular, the thesis is divided into two parts. We studied large deviations for the Landau-Lifshitz-Navier-Stokes equations and higher-order fluctuation expansions for stochastic heat equations, respectively, in order to show the consistency of fluctuating hydrodynamic equations and interacting particle systems. Moreover, we provide relationships between probabilistic phenomena and the regularity features of deterministic or stochastic partial differential equations.